Right Bol Loop 16.13.2.8 of order 16


0123456789101112131415
1014131112915106345827
2901210131514117483516
3101215914111304162758
4111014015131293217685
5121391501011148671234
6141511131009121538472
7159101211140132854361
8131101491210155726143
9274381650111310121514
1034126587120149151113
1148217356139015141012
1253671842101415091311
1385762431111591401210
1461583724151210131109
1576854213141312111090

Centre:   0   15

Centrum:   0   15

Nucleus:   0   15

Left Nucleus:   0   15

Middle Nucleus:   0   15

Right Nucleus:   0   15


Comm(L):   This graph has as its 7 vertices the nontrivial cosets of the centre. Edges represent non-commuting cosets.


1 Element of order 1:   0

13 Elements of order 2:   1   2   4   5   6   7   9   10   11   12   13   14   15

2 Elements of order 4:   3   8

Commutator Subloop:   0   15

Associator Subloop:   0   15

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (1-1)(4-1) neq (1*4)-1

Al Property:   FAILS. The left inner mapping L1,1 = (3,8)(10,13) is not an automorphism.   L1,1(2*3) neq L1,1(2)*L1,1(3)

Ar Property:   HOLDS (i.e. every right inner mapping Ra,b is an automorphism)

Right (Left, Full) Mult Group Orders:   128 (1024, 2048)


/ revised October, 2001